Yahoo Encyclopedia, 2003, defines electro magnetic induction as the production of EMF in a conductor as a result of a changing magnetic field around the conductor.
According to the Handbook of Transformer Design and Applications, by William M. Flanagan (1993), “Transformers are passive devices for transforming voltage and current.”
U.S. Pat. No. 6,879,224B2 teaches that “Inductors (L) and capacitors (C) are universally used in electronics for numerous functions. One function is to provide low loss impedance transformation.” The patent states further, “The impedance of each section is a function of the inductance and the capacitance. Specifically
  Z  =                    L        C              .  At the frequency of resonance, the resonator is a short circuit. The resonator frequency is a function of L and C.”
Nikola Tesla stated:
“The magnitude of the resonance effect depends, under otherwise equal conditions, on the quantity of electricity set in motion or on the strength of the current driven through the circuit. But the circuit opposes the passage of the current by reason of its impedance and therefore, to secure the best action it is necessary to reduce the impedance to a minimum . . . . But when the frequency of the impulses is great, the flow of the current is practically determined by self-induction. Now self-induction can be overcome by combining it with capacity. If the relation between these is such, that at the frequency used they annul each other, that is, have such values as to satisfy the condition of resonance, and the greatest quantity of electricity is made to flow through the external circuit, then the best result is obtained.”
Britannica Online defines a transformer as a “device that transfers electric energy from one alternating-current circuit to one or more other circuits, either increasing (stepping up) or reducing (stepping down) the voltage.”
U.S. Pat. No. 6,879,237 teaches, “When saturation occurs, the magnetizing current can increase in great proportions and produce an excessive heating of the windings. ‘Further’ in these structures, there are also important magnetic stray fields and leakage flux which circulate in the external environment of the device and can induce parasitic perturbations in electrical or electronic circuits . . . .”
Colonel William T. McLyman in his book Transformer and Inductor Design Handbook relates the following: “Transformer efficiency, regulation, and temperature rise are all interrelated. Not all of the input power to the transformer is delivered to the load. The difference between input power and output power is converted into heat. This power loss can be broken down into two components: core loss, Pce and copper loss, Pcu. The core loss is a fixed loss, and the copper loss is a variable loss that is related to the current demand of the load. The copper loss increases by the square of the current and also is termed a quadratic loss. Maximum efficiency is achieved when the fixed loss is equal to the quadratic loss at rated load. Transformer regulation, a, is the copper loss, Pcu divided by the output power, Po.
  a  =                    P        cu                    P        o              ⁢                  (        100        )            ⁡              [        %        ]            
The efficiency of a transformer is a good way to measure the effectiveness of the design. Efficiency is defined as the ratio of the output power, Po to the input power, PIN. The difference between, Po and, PIN is due to losses. The total power loss, PΣ, in the transformer is determined by the fixed losses in the core and the quadratic losses in the windings or copper. Thus,PΣ=Pfe+Pcu2[watts]Where Pfe is the core loss, and Pcu is the copper loss. Maximum efficiency is achieved when the fixed loss is made equal to the quadratic loss.
In the magnetic circuit, the non-harmonic relationship of the core's internal and external dimensions and/or material causes magnetic impedance of the wave (sine, square, sawtooth, etc.) because of the wave being cut off and/or deflected at a partial of itself or harmonic within the magnetic material and/or air space. In order to have the most efficient transformer design, all components must have an harmonic relationship to each other as well as the electrical characteristics of the system with which the transformer operates.
U.S. patent application Ser. No. 10/959,457 teaches according to investigations that the inventors have undertaken, that while it appears that attempts have been made to use resonance characteristics advantageously in areas such as radio modulation and audio, in power systems precisely the opposite approach has been taken, as witnessed by the numerous attempts to reduce or eliminate resonance. From what the inventors have been able to determine, the transient nature of resonance has led to the perception that resonance is undesirable in power generation and transmission systems. Resonance has led to power spikes, which can be damaging to electrical equipment.
Because there are efficiencies to be obtained from the power levels resulting from resonance, it would be desirable to determine how to make resonance a persistent, rather than a transient phenomenon.
Another well known factor is the use of hazardous materials (oil for example) as a means of dissipating heat both in overhead and underground facilities using transformers. It is possible to reduce this use of hazardous materials through substantial reduction of the heat factor.